An Inversion Formula for Orlicz Norms and Sequences of Random Variables

2012/04/05 by Soeren Christensen, Joscha Prochno, Christensen, Soeren +3
Mathematics · #46B09 #60E15 #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR) #math.FA #math.PR #msc:46B09 #msc:60E15

paper · pdf · doi:10.48550/arxiv.1204.1242

11 pages

arxiv created 2012/04/05 · arxiv updated 2012/04/06

Abstract

Given an Orlicz function M, we show which random variables ξ_i, i=1,...,n generate the associated Orlicz norm, i.e., which random variables yield 𝔼 max_{1≤ i ≤ n}|x_iξ_i| ∼ \norm(x_i)_i=1ⁿ_M. As a corollary we obtain a representation for the distribution function in terms of M and M' which can be easily applied to many examples of interest.

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